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Reply to “Backward Error Analysis ...”

  • Lutz Kettner
  • Kurt Mehlhorn
  • Sylvain Pion
  • Stefan Schirra
  • Chee Yap
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3980)

Abstract

The algorithms of computational geometry are designed for a machine model with exact real arithmetic. Substituting floating-point arithmetic for the assumed real arithmetic may cause implementations to fail. Although this is well known, it is not common knowledge. There is no paper that systematically discusses what can go wrong and provides simple examples for the di.erent ways in which floating-point implementations can fail. Due to this lack of examples, instructors of computational geometry have little material for demonstrating the inadequacy of floating-point arithmetic for geometric computations, students of computational geometry and implementers of geometric algorithms still underestimate the seriousness of the problem, and researchers in our and neighboring disciplines still believe that simple approaches are able to overcome the problem. In this paper, we study simple algorithms for two simple geometric problems, namely computing convex hulls and triangulations of point sets, and show how they can fail and explain why they fail when executed with floating-point arithmetic.

Keywords

Computational Geometry Geometric Computation Approximate Algorithm Geometric Problem Geometric Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Lutz Kettner
    • 1
  • Kurt Mehlhorn
    • 1
  • Sylvain Pion
    • 1
  • Stefan Schirra
    • 1
  • Chee Yap
    • 1
  1. 1.No institute 

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